An axisymmetric tangent stress is applied to a lateral surface of a multilayered elastic finite cylinder with a fixed bottom face. The problem is solved for an arbitrary number of layers. The layers are coaxial, and t...An axisymmetric tangent stress is applied to a lateral surface of a multilayered elastic finite cylinder with a fixed bottom face. The problem is solved for an arbitrary number of layers. The layers are coaxial, and the conditions of an ideal mechanical contact are fulfilled between them. A circular crack is situated parallel to the cylinder’s faces in the internal layer with branches free from stress. The upper face of the cylinder is also free from stress. Concretization of the problem is done on examples of two-and three-layered cylinders. An analysis of cylinders’ stress state is conducted and the stress intensity factor is evaluated depending on the crack’s geometry, its location and ratio of the shear modulus. Advantages of the proposed method include reduction of the solution constants’ number regardless of the number of layers, and presentation of the mechanical characteristics in a form of uniformly convergent series.展开更多
基金Project supported by the Ukrainian Department of Science and Education(No.0115U003211)
文摘An axisymmetric tangent stress is applied to a lateral surface of a multilayered elastic finite cylinder with a fixed bottom face. The problem is solved for an arbitrary number of layers. The layers are coaxial, and the conditions of an ideal mechanical contact are fulfilled between them. A circular crack is situated parallel to the cylinder’s faces in the internal layer with branches free from stress. The upper face of the cylinder is also free from stress. Concretization of the problem is done on examples of two-and three-layered cylinders. An analysis of cylinders’ stress state is conducted and the stress intensity factor is evaluated depending on the crack’s geometry, its location and ratio of the shear modulus. Advantages of the proposed method include reduction of the solution constants’ number regardless of the number of layers, and presentation of the mechanical characteristics in a form of uniformly convergent series.
